Yes. After you put the menu item in your "cart", it will lists the items that can be removed (like cheese or mayo), and ask you if you want to modify these items. I was able to remove mayo/sauce on different items and I remember seeing options about cheese. Oh course if you have any problems or something isn't listed, you can talk to a CM.
Btw, we loved the contempo cafe's unique items. I liked the mahi sandwich, but my favorite was the hot roast beef. My DH loved the hot turkey sandwich that has apples & apple butter on it. He had it 3 times